Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbifold curves

In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbifold curves and establish the isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. In the specific example of a twisted projective line, isomorphisms between the space of g-twisted (restricted) conformal block and the space of g-twisted (restricted) correlation functions are established. This leads to a more conceptual proof of the g-twisted fusion rule theorem in vertex operator algebra theory. Furthermore, by introducing a geometric generalization of Zhu's algebra and its modules, we obtain a general version of the twisted fusion rule theorem.